Turkey sent out an official warning to other vessels to avoid the area.
Greece announced its exercises after Turkey said it would extend a mission by a seismic research ship.
Germany is sending its Foreign Minister Heiko Maas to Athens and Ankara on Tuesday to try to reduce tension.
Mr. Maas is due to meet Greek Prime Minister Kyriakos Mitsotakis before talks in Ankara with his Turkish counterpart.
Turkey and Greece – both Nato members – are at loggerheads over the discovery of oil and gas deposits off Crete and Cyprus in disputed waters.
Greece is in the European Union, which has called for dialogue. But France appears to side with Greece – it has been involved in a recent naval exercise with Greece.
Turkey announced on Monday that exploration by its Oruc Reis research vessel in contentious waters would be extended for four days till 27 August. That appears to have spurred Greece, which sees the survey as unlawful, to signal naval exercises.